He added that the threat of a Republican takeover of the chamber is becoming more real as outside conservative groups pour money into tight races. Organizations led by the Koch-backed Americans for Prosperity super PAC, for example, have spent more than $20 million on commercials targeting Democrats in Senate races across the country.

"We're faced with a grim reality that more money is being spent earlier in some of these hot races than we've ever seen," Durbin said. "We're spending some, but we can't keep up with them."

Veteran Democratic strategist David Axelrod agrees.

"This is a serious threat," Axelrod told the Times. "It would behoove Democratic activists and donors who are whipped up about 2016 to shift their focus, or they may be sitting here in November, looking at a Republican Senate to go along with the House."

Sens. Mitch McConnell and John Cornyn, both of whom are facing tough primary challenges this year, were two of the lawmakers who chose to votefor a "clean" debt ceiling bill last week at the risk of inflaming tea party ire.

"It was not an easy exercise, but it keeps the focus on the issues we want to be on," Arizona GOP Sen. John McCain told the Times. He said by avoiding a fight on the debt issue, Republicans removed an opportunity for the Democrats to portray them as reckless.

"We dodged a bullet here," McCain added.

Democrats are also concerned about the bungled rollout of Obamacare.

"People see national polling, and maybe the national polling is getting a little bit tougher, so they get nervous," Virginia Democratic Sen. Tim Kaine told the Times. "But at the end of the day, it ain't about national polling. It's about individual races."